Geometric Diagram of Triangle and Circle

This geometric diagram illustrates a triangle with its incenter, denoted as 'I'. It clearly shows the angle bisectors, marked with angles such as α/2 and β/2, converging at 'I'. The inradius 'r' is depicted as a perpendicular segment from 'I' to a side. A circle centered at 'I' has its radius labeled 'R-d', extending to one of the triangle's vertices. Additionally, a segment from 'I' to point 'U' on an angle bisector is labeled 'd', suggesting a specific geometric relationship or proof step.

geometry - triangle - incenter - inradius - angle bisector - circle - geometric diagram - mathematical - euclidean geometry